Noninvasive diagnoses using interrogating signals are frequently employed to ascertain the condition of tissue and functional parameters of organs. Such interrogating signals may use, for example, electromagnetic or sonic, including ultrasonic, energy. One example is transmitting ultrasonic waves into an organism, such as a human being, and receiving a return signal that is a modified version of the transmitted interrogating signal, with the modifications caused by the properties of one or more tissue types. The received signal is measured and processed to evaluate the condition or properties of the tissue(s) or other material(s) with which the interrogating signal interacts. In particular, interrogating ultrasonic signals are often transmitted into an organism and the received signal is due to backscattering or echos of the interrogating signal by one or more tissue types. Even more particularly, an ultrasonic interrogating signal is often transmitted into a region of the organism where blood flow is expected and the received signal is a modified version of the interrogating signal wherein such modifications are due in whole or part to frequency shifts caused by Doppler effects caused by movement of tissues, including movement of blood. In this case it is desirable to measure and process the received signal in a manner such that the amount of Doppler frequency shift that occurs can be ascertained in order to estimate the various velocities of the moving tissue, particularly the velocities of the flowing blood.
Ultrasonic Doppler techniques typically entail using a hand-held probe that contains one or more transducers that are used to transmit the interrogating signal and to produce a response, typically in the form of a time-varying voltage, to the received signal. The interrogating ultrasonic signal typically has a frequency in the radio frequency (RF) range of about 0.5 million Hertz (0.5 MHz) to about 20 MHz, although other frequencies may be used. The interrogating signal may be sent continuously, in which case the method employed is termed “continuous wave” (CW) or the interrogating signal may be sent intermittently, usually on a periodic basis, in which case the method employed is termed “pulsed.” When pulsed Doppler is used it is possible to interrogate tissue over a range of specified distances from the transducers by measuring the received signal only for a selected duration that occurs after a predetermined time delay after the pulse is sent. If the speed of sound for the intervening tissue is known then the time delay converts directly into a depth of tissue being interrogated. Interrogating a specified tissue depth often provides clinically valuable information that cannot be obtained if CW Doppler is used. CW Doppler systems are often simpler than pulsed Doppler systems, although they cannot provide information that is known to come from tissue associated with a specific time delay (and corresponding estimated tissue depth).
Regardless of whether the Doppler system is pulsed or continuous, the spectral content of the received signal is analyzed to assess how the tissue modified the interrogating signal. The spectral frequency content of the signal is a measure of the amplitudes of each of the constituent frequencies that, when combined, form the total signal. The spectral content is typically represented as either the amplitude of each of the frequencies or as the power of each of the frequencies. When the spectral content data are graphed the resulting graphs have a variety of names including spectrograms and spectral density functions. The term “spectral density function” (SD function) will be used as the general term below. When the frequency content of the interrogating signal is known it can be compared to the spectrum of the received signal and the differences between the spectra can be interpreted as arising from the velocity profiles of the tissues through which the signals passed. The velocity profiles can be back-calculated from spectral differences using established methods that are well known.
To date, a variety of methods have been used to estimate the spectral frequency content of the received signals. The main spectral analysis methods are traditionally classified as being either nonparametric or parametric methods.
The nonparametric methods are related to using Fourier series and they estimate the spectral content at equally spaced frequency points. The extant methods include Fourier and z-transform (including the Chirp z-transform). For brevity, all methods which employ assessing spectral content at equally spaced frequency points are referred to as Fourier methods.
Fourier methods, typically in the form of fast Fourier transforms (FFT), are well known and decompose a signal into frequencies that are integral multiples of a fundamental frequency. The integral multiple frequencies form an orthogonal basis in the frequency domain. This information can be used to approximate the signal as a trigonometric polynomial, as is well known. Fourier methods have been widely used to analyze the received signal because such methods have been refined to the point where they are fast and have well defined properties.
The other class of spectral analysis methods are parametric methods. Parametric methods use time-series analysis to estimate the parameters for a rational function model. The rational function can have either only poles, which is an autoregressive (AR) model, only zeros, which is a moving average (MA) model, or both poles and zeros, which is an autoregressive-moving average (ARMA) model. Included in these methods are maximum entropy methods (MEM). The number of model parameters used in a parametric method is termed the order of the model. The various methods that exist for calculating the values of the model parameters, such as the Burg algorithm and Durbin's first and second methods, are well known. An advantage of parametric methods is that they can produce reasonable spectral estimates using very few cycles or fractions of cycles of data.